How do I scale an object proportionally using numbers on the scale panel?
By left-clicking and dragging down on the sliders you can select and edit the values for multiple axes simultaneously:



Alternatively, if you want to do things with keyboard shortcuts you can press S and drag, that will scale your object (or selected vertices, depending on what mode you are on) in all axes.

To constrain transformations on a single axis you can do SX to scale on the X axis only, or SShiftZ to scale on X and Y only (but not on Z)